Welcome to the NBS board.
Come down to Petaluma and talk to Gabe at Sportsman's Arms. Address is in the Sonoma County Gun Dealer's thread in the "Get Connected" forum. He is a great guy, easy to deal with and is always happy to answer questions.
There are no public ranges, indoor or outdoor in Sonoma County. Only government facilities and private clubs. There are a couple of ad hoc shooting areas, and there are some ranches that have sufficient land to have their own range for friends and family. Closest public indoor range is Bullseye down in San Rafael,
http://www.bullseyerange.com/. Closest public outdoor range is Circle S, which is west of Petaluma and just across the line into Marin County.
Sportsman's Arms is, coincidentally, right on the way to Circle S.

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"A gun is as good or as bad as the man using it. Remember that. "